-LRB- CNN -RRB- -- Comedian Joan Rivers is `` resting comfortably '' in a New York hospital after apparently suffering cardiac and respiratory arrest during a procedure at a medical clinic Thursday .

Her daughter , Melissa Rivers , issued a statement Thursday night after arriving at the hospital following a flight from Los Angeles .

`` I want to thank everyone for the overwhelming love and support for my mother . She is resting comfortably and is with our family . We ask that you continue to keep her in your thoughts and prayers , '' she said .

A law enforcement official told CNN that Rivers stopped breathing during throat surgery . Rivers , 81 , was taken by ambulance in critical condition to Mount Sinai Hospital in New York City .

The clinic address given by a New York Fire Department spokesman is a building that houses an endoscopy clinic where doctors perform minor procedures on patients . The clinic is a mile away from the hospital .

`` This morning , Joan Rivers was taken to the Mount Sinai Hospital in New York , where she is being attended to , '' hospital spokesman Sid Dinsay said in a statement . `` Her family wants to thank everybody for their outpouring of love and support . We will provide an update on her condition as it becomes available . ''

Rivers had been scheduled to perform her comedy act at the Count Basie Theater in Red Bank , New Jersey , Friday night .

Michael Lucas , who was in the audience for Rivers ' show at New York 's Beechman Theater Wednesday night , told CNN that she joked about death .

`` She said , ` You know I 'm 81 years old , and I could drop dead at any moment and you would be so lucky because you will have a story to tell your friends for the rest of your life , ' '' Lucas said . `` Then she mimicked people talking about what it was like to see her drop dead on stage . ''

Rivers was in fine form , he said . `` There was no sign -LRB- Wednesday -RRB- night that she was declining . Her show was over an hour long and she never stumbled or even paused to catch her breath . ''

In 2013 , Rivers allowed cameras to record a health scare for her and her daughter 's reality show , `` Joan & Melissa : Joan Knows Best ? ''

Rivers said on the show that doctors found a spot on an X-ray after she had a persistent cough .

`` We 're just not going to be sad about this , '' Rivers said during the episode . `` We 're gon na do jokes and be up until we know . That 's how I deal with things . I 'm not just gon na sit around the next couple of days and go crazy . ''

Rivers has been open about her health issues . She was diagnosed with osteoporosis in 2002 after a fall down some stairs left her with broken bones , and she became an advocate for screenings for women .

She also admitted to not being as healthy as she could be .

`` I try not to be , but I 'm a terrible eater , '' she said . `` I wish I could say I eat super-healthy , but I do n't . I love junk food -- it should be its own food group -- so I help my bones with supplements and medicine . ''

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See more comedian content at CNN Comedy .

CNN 's Tony Marco , Lisa Respers France and Doug Ganley contributed to this report .

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NEW : Rivers ' daughter and grandson arrive at hospital after flight from Los Angeles

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Joan Rivers stopped breath during a procedure at a medical clinic

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Her reality show documented a health scare last year

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She has been open about previous health issues